My father has just passed away. He had drawn up his own will and then entrusted it to his notary. For the settlement of the succession, is the depositary notary obliged to record the opening of the will on death and if so, within what time frame?

Yes. The law provides that the notary depositary of the holographic will, draws up a report "on the spot" of the opening and status of the will, specifying the circumstances of its deposit.
The original of the will is appended to the minutes. These documents are then maintained in the notary's archives.
In the month following the establishment of the minutes, the notary must send a copy of the report as well as a copy of the will to the registry of the judicial court of the place of opening of the succession.